Robert Heinlein did not invent the term "hush-a-phone" - but he did expand on the original device with futuristic attachments.

Shortly thereafter the first wave flushed another technician. He was on the far side of a rotor; they
were almost on him before he was, seen. He did not attempt to resist, although he was armed, and the incident would not have been worth recording, had he not been talking into a hush-a-phone which he had plugged into the telephone jack at the base of the rotor.

Gaines reached the group as the capture was being effected. He snatched at the soft rubber mask of the phone, jerking it away from the man's mouth so violently that he could feel the bone-conduction receiver grate between the man's teeth. The prisoner spat out a piece of broken tooth and glared, but ignored attempts to question him.

The original Hush-a-Phone was first manufactured and sold in 1921. It was a very simple device that provided privacy, avoided annoying other people and helped you hear better. It had versions for pedestal phones as well as those new-fangled handsets. It was a very simple device that just slipped onto the phone; it had no moving parts or electrical components.

Heinlein, however, has added some improvements. The rubber mask improves noise suppression; the bone-conduction receiver means that none of the other person's part of the conversation ever goes out in the open air.